%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : RNG105+1 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n023.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 13:57:54 EDT 2023 % Result : Theorem 61.40s 8.81s % Output : Proof 61.92s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.13 % Problem : RNG105+1 : TPTP v8.1.2. Released v4.0.0. % 0.03/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n023.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Sun Aug 27 02:44:11 EDT 2023 % 0.12/0.34 % CPUTime : % 0.49/0.60 ________ _____ % 0.49/0.60 ___ __ \_________(_)________________________________ % 0.49/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.49/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.49/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.49/0.60 % 0.49/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.49/0.60 (2023-06-19) % 0.49/0.60 % 0.49/0.60 (c) Philipp Rümmer, 2009-2023 % 0.49/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.49/0.60 Amanda Stjerna. % 0.49/0.60 Free software under BSD-3-Clause. % 0.49/0.60 % 0.49/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.49/0.60 % 0.49/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.49/0.62 Running up to 7 provers in parallel. % 0.70/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.70/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.70/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.70/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.70/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.70/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.70/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.27/1.18 Prover 4: Preprocessing ... % 3.27/1.18 Prover 1: Preprocessing ... % 3.27/1.23 Prover 3: Preprocessing ... % 3.27/1.23 Prover 5: Preprocessing ... % 3.27/1.23 Prover 0: Preprocessing ... % 3.27/1.23 Prover 2: Preprocessing ... % 3.27/1.23 Prover 6: Preprocessing ... % 10.48/2.17 Prover 1: Constructing countermodel ... % 11.35/2.27 Prover 3: Constructing countermodel ... % 12.17/2.36 Prover 5: Proving ... % 12.17/2.37 Prover 6: Proving ... % 13.52/2.56 Prover 2: Proving ... % 14.32/2.66 Prover 4: Constructing countermodel ... % 14.90/2.74 Prover 0: Proving ... % 23.25/3.84 Prover 3: gave up % 23.47/3.86 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 24.50/4.00 Prover 7: Preprocessing ... % 26.88/4.30 Prover 7: Constructing countermodel ... % 32.81/5.08 Prover 1: gave up % 32.81/5.10 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 33.57/5.21 Prover 8: Preprocessing ... % 36.41/5.56 Prover 8: Warning: ignoring some quantifiers % 36.41/5.57 Prover 8: Constructing countermodel ... % 53.33/7.76 Prover 8: gave up % 53.68/7.77 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 54.48/7.89 Prover 9: Preprocessing ... % 57.56/8.31 Prover 2: stopped % 57.56/8.32 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 58.86/8.43 Prover 10: Preprocessing ... % 59.86/8.57 Prover 9: Constructing countermodel ... % 59.86/8.60 Prover 10: Constructing countermodel ... % 61.40/8.77 Prover 10: Found proof (size 62) % 61.40/8.77 Prover 10: proved (452ms) % 61.40/8.77 Prover 9: stopped % 61.40/8.77 Prover 5: stopped % 61.40/8.77 Prover 6: stopped % 61.40/8.77 Prover 4: stopped % 61.40/8.77 Prover 7: stopped % 61.40/8.81 Prover 0: stopped % 61.40/8.81 % 61.40/8.81 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 61.40/8.81 % 61.40/8.82 % SZS output start Proof for theBenchmark % 61.40/8.82 Assumptions after simplification: % 61.40/8.82 --------------------------------- % 61.40/8.82 % 61.40/8.82 (mAMDistr) % 61.73/8.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 61.73/8.85 $i] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ % 61.73/8.85 (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 61.73/8.85 aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v6: $i] : ? [v7: % 61.73/8.85 $i] : ? [v8: $i] : ? [v9: $i] : (sdtasdt0(v6, v0) = v7 & sdtasdt0(v2, % 61.73/8.85 v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v8, % 61.73/8.85 v9) = v7 & sdtpldt0(v1, v2) = v6 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 61.73/8.85 $i(v5))) % 61.73/8.85 % 61.73/8.85 (mAddComm) % 61.73/8.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 61.73/8.85 $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aElement0(v0) | (sdtpldt0(v1, v0) % 61.73/8.85 = v2 & $i(v2))) % 61.73/8.85 % 61.73/8.85 (mDefPrIdeal) % 61.73/8.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (slsdtgt0(v0) = % 61.73/8.86 v1) | ~ (sdtasdt0(v0, v3) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 61.73/8.86 $i(v0) | ~ aElement0(v3) | ~ aElement0(v0) | aElementOf0(v2, v1)) & ! % 61.73/8.86 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (slsdtgt0(v0) = v1) | ~ % 61.73/8.86 $i(v2) | ~ $i(v0) | ~ aSet0(v2) | ~ aElement0(v0) | ? [v3: $i] : ? [v4: % 61.73/8.86 $i] : ? [v5: $i] : ($i(v4) & $i(v3) & ( ~ aElementOf0(v3, v2) | ! [v6: % 61.73/8.86 $i] : ( ~ (sdtasdt0(v0, v6) = v3) | ~ $i(v6) | ~ aElement0(v6))) & % 61.73/8.86 (aElementOf0(v3, v2) | (v5 = v3 & sdtasdt0(v0, v4) = v3 & % 61.73/8.86 aElement0(v4))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 61.73/8.86 (slsdtgt0(v0) = v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2, % 61.73/8.86 v1) | ~ aElement0(v0) | ? [v3: $i] : (sdtasdt0(v0, v3) = v2 & $i(v3) & % 61.73/8.86 aElement0(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (slsdtgt0(v0) = v1) | ~ % 61.73/8.86 $i(v1) | ~ $i(v0) | ~ aElement0(v0) | aSet0(v1)) % 61.73/8.86 % 61.73/8.86 (mMulComm) % 61.73/8.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 61.73/8.86 $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aElement0(v0) | (sdtasdt0(v1, v0) % 61.73/8.86 = v2 & $i(v2))) % 61.73/8.86 % 61.73/8.86 (mSortsB) % 61.73/8.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 61.73/8.86 $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aElement0(v0) | aElement0(v2)) % 61.73/8.86 % 61.73/8.86 (mSortsB_02) % 61.73/8.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 61.73/8.86 $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aElement0(v0) | aElement0(v2)) % 61.73/8.86 % 61.73/8.86 (m__) % 61.73/8.86 $i(xz) & $i(xy) & $i(xx) & $i(xc) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 61.73/8.86 (slsdtgt0(xc) = v1 & $i(v1) & ((sdtasdt0(xz, xx) = v2 & $i(v2) & ~ % 61.73/8.86 aElementOf0(v2, v1)) | (sdtpldt0(xx, xy) = v0 & $i(v0) & ~ % 61.73/8.86 aElementOf0(v0, v1)))) % 61.73/8.86 % 61.73/8.86 (m__1905) % 61.73/8.87 $i(xc) & aElement0(xc) % 61.73/8.87 % 61.73/8.87 (m__1933) % 61.73/8.87 $i(xz) & $i(xy) & $i(xx) & $i(xc) & ? [v0: $i] : (slsdtgt0(xc) = v0 & $i(v0) % 61.73/8.87 & aElementOf0(xy, v0) & aElementOf0(xx, v0) & aElement0(xz)) % 61.73/8.87 % 61.73/8.87 (m__1956) % 61.73/8.87 sdtasdt0(xc, xu) = xx & $i(xu) & $i(xx) & $i(xc) & aElement0(xu) % 61.73/8.87 % 61.73/8.87 (m__1979) % 61.73/8.87 sdtasdt0(xc, xv) = xy & $i(xv) & $i(xy) & $i(xc) & aElement0(xv) % 61.73/8.87 % 61.73/8.87 (m__2010) % 61.73/8.87 $i(xv) & $i(xu) & $i(xy) & $i(xx) & $i(xc) & ? [v0: $i] : ? [v1: $i] : % 61.73/8.87 (sdtasdt0(xc, v1) = v0 & sdtpldt0(xu, xv) = v1 & sdtpldt0(xx, xy) = v0 & % 61.73/8.87 $i(v1) & $i(v0)) % 61.73/8.87 % 61.73/8.87 (m__2043) % 61.73/8.87 $i(xu) & $i(xz) & $i(xx) & $i(xc) & ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xu, % 61.73/8.87 xz) = v1 & sdtasdt0(xz, xx) = v0 & sdtasdt0(xc, v1) = v0 & $i(v1) & % 61.73/8.87 $i(v0)) % 61.73/8.87 % 61.73/8.87 (function-axioms) % 61.73/8.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 61.73/8.87 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 61.73/8.87 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt1(v3, v2) = v1) | % 61.73/8.87 ~ (sdtpldt1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 61.73/8.87 [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 61.73/8.87 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 61.73/8.87 (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : ! % 61.73/8.87 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slsdtgt0(v2) = v1) | ~ (slsdtgt0(v2) % 61.73/8.87 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 61.73/8.87 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 61.73/8.87 ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ (smndt0(v2) = v0)) % 61.73/8.87 % 61.73/8.87 Further assumptions not needed in the proof: % 61.73/8.87 -------------------------------------------- % 61.92/8.88 mAddAsso, mAddInvr, mAddZero, mCancel, mChineseRemainder, mDefDiv, mDefDvs, % 61.92/8.88 mDefGCD, mDefIdeal, mDefMod, mDefRel, mDefSInt, mDefSSum, mDivision, mEOfElem, % 61.92/8.88 mElmSort, mEucSort, mIdeInt, mIdeSum, mMulAsso, mMulMnOne, mMulUnit, mMulZero, % 61.92/8.88 mNatLess, mNatSort, mSetEq, mSetSort, mSortsC, mSortsC_01, mSortsU, mUnNeZr % 61.92/8.88 % 61.92/8.88 Those formulas are unsatisfiable: % 61.92/8.88 --------------------------------- % 61.92/8.88 % 61.92/8.88 Begin of proof % 61.92/8.88 | % 61.92/8.88 | ALPHA: (mDefPrIdeal) implies: % 61.92/8.88 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 61.92/8.88 | (slsdtgt0(v0) = v1) | ~ (sdtasdt0(v0, v3) = v2) | ~ $i(v3) | ~ % 61.92/8.88 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v3) | ~ aElement0(v0) % 61.92/8.88 | | aElementOf0(v2, v1)) % 61.92/8.88 | % 61.92/8.88 | ALPHA: (m__1905) implies: % 61.92/8.88 | (2) aElement0(xc) % 61.92/8.88 | % 61.92/8.88 | ALPHA: (m__1933) implies: % 61.92/8.88 | (3) ? [v0: $i] : (slsdtgt0(xc) = v0 & $i(v0) & aElementOf0(xy, v0) & % 61.92/8.88 | aElementOf0(xx, v0) & aElement0(xz)) % 61.92/8.88 | % 61.92/8.88 | ALPHA: (m__1956) implies: % 61.92/8.88 | (4) aElement0(xu) % 61.92/8.88 | (5) sdtasdt0(xc, xu) = xx % 61.92/8.88 | % 61.92/8.88 | ALPHA: (m__1979) implies: % 61.92/8.88 | (6) aElement0(xv) % 61.92/8.88 | (7) sdtasdt0(xc, xv) = xy % 61.92/8.88 | % 61.92/8.88 | ALPHA: (m__2010) implies: % 61.92/8.88 | (8) $i(xv) % 61.92/8.88 | (9) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xc, v1) = v0 & sdtpldt0(xu, xv) = % 61.92/8.88 | v1 & sdtpldt0(xx, xy) = v0 & $i(v1) & $i(v0)) % 61.92/8.88 | % 61.92/8.88 | ALPHA: (m__2043) implies: % 61.92/8.88 | (10) $i(xu) % 61.92/8.88 | (11) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xu, xz) = v1 & sdtasdt0(xz, xx) % 61.92/8.88 | = v0 & sdtasdt0(xc, v1) = v0 & $i(v1) & $i(v0)) % 61.92/8.88 | % 61.92/8.88 | ALPHA: (m__) implies: % 61.92/8.88 | (12) $i(xc) % 61.92/8.88 | (13) $i(xz) % 61.92/8.89 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (slsdtgt0(xc) = v1 & $i(v1) % 61.92/8.89 | & ((sdtasdt0(xz, xx) = v2 & $i(v2) & ~ aElementOf0(v2, v1)) | % 61.92/8.89 | (sdtpldt0(xx, xy) = v0 & $i(v0) & ~ aElementOf0(v0, v1)))) % 61.92/8.89 | % 61.92/8.89 | ALPHA: (function-axioms) implies: % 61.92/8.89 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slsdtgt0(v2) % 61.92/8.89 | = v1) | ~ (slsdtgt0(v2) = v0)) % 61.92/8.89 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 61.92/8.89 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 61.92/8.89 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 61.92/8.89 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 61.92/8.89 | % 61.92/8.89 | DELTA: instantiating (9) with fresh symbols all_33_0, all_33_1 gives: % 61.92/8.89 | (18) sdtasdt0(xc, all_33_0) = all_33_1 & sdtpldt0(xu, xv) = all_33_0 & % 61.92/8.89 | sdtpldt0(xx, xy) = all_33_1 & $i(all_33_0) & $i(all_33_1) % 61.92/8.89 | % 61.92/8.89 | ALPHA: (18) implies: % 61.92/8.89 | (19) sdtpldt0(xx, xy) = all_33_1 % 61.92/8.89 | (20) sdtpldt0(xu, xv) = all_33_0 % 61.92/8.89 | % 61.92/8.89 | DELTA: instantiating (3) with fresh symbol all_35_0 gives: % 61.92/8.89 | (21) slsdtgt0(xc) = all_35_0 & $i(all_35_0) & aElementOf0(xy, all_35_0) & % 61.92/8.89 | aElementOf0(xx, all_35_0) & aElement0(xz) % 61.92/8.89 | % 61.92/8.89 | ALPHA: (21) implies: % 61.92/8.89 | (22) aElement0(xz) % 61.92/8.89 | (23) slsdtgt0(xc) = all_35_0 % 61.92/8.89 | % 61.92/8.89 | DELTA: instantiating (11) with fresh symbols all_37_0, all_37_1 gives: % 61.92/8.89 | (24) sdtasdt0(xu, xz) = all_37_0 & sdtasdt0(xz, xx) = all_37_1 & % 61.92/8.89 | sdtasdt0(xc, all_37_0) = all_37_1 & $i(all_37_0) & $i(all_37_1) % 61.92/8.89 | % 61.92/8.89 | ALPHA: (24) implies: % 61.92/8.89 | (25) sdtasdt0(xc, all_37_0) = all_37_1 % 61.92/8.89 | (26) sdtasdt0(xz, xx) = all_37_1 % 61.92/8.89 | (27) sdtasdt0(xu, xz) = all_37_0 % 61.92/8.89 | % 61.92/8.89 | DELTA: instantiating (14) with fresh symbols all_39_0, all_39_1, all_39_2 % 61.92/8.89 | gives: % 61.92/8.89 | (28) slsdtgt0(xc) = all_39_1 & $i(all_39_1) & ((sdtasdt0(xz, xx) = all_39_0 % 61.92/8.89 | & $i(all_39_0) & ~ aElementOf0(all_39_0, all_39_1)) | % 61.92/8.89 | (sdtpldt0(xx, xy) = all_39_2 & $i(all_39_2) & ~ % 61.92/8.89 | aElementOf0(all_39_2, all_39_1))) % 61.92/8.89 | % 61.92/8.89 | ALPHA: (28) implies: % 61.92/8.89 | (29) $i(all_39_1) % 61.92/8.89 | (30) slsdtgt0(xc) = all_39_1 % 61.92/8.89 | (31) (sdtasdt0(xz, xx) = all_39_0 & $i(all_39_0) & ~ aElementOf0(all_39_0, % 61.92/8.89 | all_39_1)) | (sdtpldt0(xx, xy) = all_39_2 & $i(all_39_2) & ~ % 61.92/8.89 | aElementOf0(all_39_2, all_39_1)) % 61.92/8.89 | % 61.92/8.89 | GROUND_INST: instantiating (15) with all_35_0, all_39_1, xc, simplifying with % 61.92/8.89 | (23), (30) gives: % 61.92/8.90 | (32) all_39_1 = all_35_0 % 61.92/8.90 | % 61.92/8.90 | REDUCE: (29), (32) imply: % 61.92/8.90 | (33) $i(all_35_0) % 61.92/8.90 | % 61.92/8.90 | GROUND_INST: instantiating (mSortsB) with xu, xv, all_33_0, simplifying with % 61.92/8.90 | (4), (6), (8), (10), (20) gives: % 61.92/8.90 | (34) aElement0(all_33_0) % 61.92/8.90 | % 61.92/8.90 | GROUND_INST: instantiating (mSortsB_02) with xc, xu, xx, simplifying with (2), % 61.92/8.90 | (4), (5), (10), (12) gives: % 61.92/8.90 | (35) aElement0(xx) % 61.92/8.90 | % 61.92/8.90 | GROUND_INST: instantiating (mMulComm) with xc, xu, xx, simplifying with (2), % 61.92/8.90 | (4), (5), (10), (12) gives: % 61.92/8.90 | (36) sdtasdt0(xu, xc) = xx & $i(xx) % 61.92/8.90 | % 61.92/8.90 | ALPHA: (36) implies: % 61.92/8.90 | (37) sdtasdt0(xu, xc) = xx % 61.92/8.90 | % 61.92/8.90 | GROUND_INST: instantiating (mAMDistr) with xc, xu, xv, xx, xy, all_33_1, % 61.92/8.90 | simplifying with (2), (4), (5), (6), (7), (8), (10), (12), (19) % 61.92/8.90 | gives: % 61.92/8.90 | (38) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v0, % 61.92/8.90 | xc) = v1 & sdtasdt0(xv, xc) = v3 & sdtasdt0(xu, xc) = v2 & % 61.92/8.90 | sdtasdt0(xc, v0) = all_33_1 & sdtpldt0(v2, v3) = v1 & sdtpldt0(xu, % 61.92/8.90 | xv) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_33_1)) % 61.92/8.90 | % 61.92/8.90 | GROUND_INST: instantiating (mSortsB_02) with xc, xv, xy, simplifying with (2), % 61.92/8.90 | (6), (7), (8), (12) gives: % 61.92/8.90 | (39) aElement0(xy) % 61.92/8.90 | % 61.92/8.90 | GROUND_INST: instantiating (mMulComm) with xc, xv, xy, simplifying with (2), % 61.92/8.90 | (6), (7), (8), (12) gives: % 61.92/8.90 | (40) sdtasdt0(xv, xc) = xy & $i(xy) % 61.92/8.90 | % 61.92/8.90 | ALPHA: (40) implies: % 61.92/8.90 | (41) sdtasdt0(xv, xc) = xy % 61.92/8.90 | % 61.92/8.90 | GROUND_INST: instantiating (mSortsB_02) with xu, xz, all_37_0, simplifying % 61.92/8.90 | with (4), (10), (13), (22), (27) gives: % 61.92/8.90 | (42) aElement0(all_37_0) % 61.92/8.90 | % 61.92/8.90 | GROUND_INST: instantiating (mMulComm) with xu, xz, all_37_0, simplifying with % 61.92/8.90 | (4), (10), (13), (22), (27) gives: % 61.92/8.90 | (43) sdtasdt0(xz, xu) = all_37_0 & $i(all_37_0) % 61.92/8.90 | % 61.92/8.90 | ALPHA: (43) implies: % 61.92/8.90 | (44) $i(all_37_0) % 61.92/8.90 | % 61.92/8.90 | DELTA: instantiating (38) with fresh symbols all_58_0, all_58_1, all_58_2, % 61.92/8.90 | all_58_3 gives: % 61.92/8.91 | (45) sdtasdt0(all_58_3, xc) = all_58_2 & sdtasdt0(xv, xc) = all_58_0 & % 61.92/8.91 | sdtasdt0(xu, xc) = all_58_1 & sdtasdt0(xc, all_58_3) = all_33_1 & % 61.92/8.91 | sdtpldt0(all_58_1, all_58_0) = all_58_2 & sdtpldt0(xu, xv) = all_58_3 % 61.92/8.91 | & $i(all_58_0) & $i(all_58_1) & $i(all_58_2) & $i(all_58_3) & % 61.92/8.91 | $i(all_33_1) % 61.92/8.91 | % 61.92/8.91 | ALPHA: (45) implies: % 61.92/8.91 | (46) $i(all_58_3) % 61.92/8.91 | (47) $i(all_58_1) % 61.92/8.91 | (48) $i(all_58_0) % 61.92/8.91 | (49) sdtpldt0(xu, xv) = all_58_3 % 61.92/8.91 | (50) sdtpldt0(all_58_1, all_58_0) = all_58_2 % 61.92/8.91 | (51) sdtasdt0(xc, all_58_3) = all_33_1 % 61.92/8.91 | (52) sdtasdt0(xu, xc) = all_58_1 % 61.92/8.91 | (53) sdtasdt0(xv, xc) = all_58_0 % 61.92/8.91 | % 61.92/8.91 | GROUND_INST: instantiating (16) with all_33_0, all_58_3, xv, xu, simplifying % 61.92/8.91 | with (20), (49) gives: % 61.92/8.91 | (54) all_58_3 = all_33_0 % 61.92/8.91 | % 61.92/8.91 | GROUND_INST: instantiating (17) with xx, all_58_1, xc, xu, simplifying with % 61.92/8.91 | (37), (52) gives: % 61.92/8.91 | (55) all_58_1 = xx % 61.92/8.91 | % 61.92/8.91 | GROUND_INST: instantiating (17) with xy, all_58_0, xc, xv, simplifying with % 61.92/8.91 | (41), (53) gives: % 61.92/8.91 | (56) all_58_0 = xy % 61.92/8.91 | % 61.92/8.91 | REDUCE: (51), (54) imply: % 61.92/8.91 | (57) sdtasdt0(xc, all_33_0) = all_33_1 % 61.92/8.91 | % 61.92/8.91 | REDUCE: (50), (55), (56) imply: % 61.92/8.91 | (58) sdtpldt0(xx, xy) = all_58_2 % 61.92/8.91 | % 61.92/8.91 | REDUCE: (48), (56) imply: % 61.92/8.91 | (59) $i(xy) % 61.92/8.91 | % 61.92/8.91 | REDUCE: (47), (55) imply: % 61.92/8.91 | (60) $i(xx) % 61.92/8.91 | % 61.92/8.91 | REDUCE: (46), (54) imply: % 61.92/8.91 | (61) $i(all_33_0) % 61.92/8.91 | % 61.92/8.91 | GROUND_INST: instantiating (16) with all_33_1, all_58_2, xy, xx, simplifying % 61.92/8.91 | with (19), (58) gives: % 61.92/8.91 | (62) all_58_2 = all_33_1 % 61.92/8.91 | % 61.92/8.91 | GROUND_INST: instantiating (mAddComm) with xx, xy, all_33_1, simplifying with % 61.92/8.91 | (19), (35), (39), (59), (60) gives: % 61.92/8.91 | (63) sdtpldt0(xy, xx) = all_33_1 & $i(all_33_1) % 61.92/8.91 | % 61.92/8.91 | ALPHA: (63) implies: % 61.92/8.91 | (64) $i(all_33_1) % 61.92/8.91 | % 61.92/8.91 | GROUND_INST: instantiating (1) with xc, all_35_0, all_33_1, all_33_0, % 61.92/8.91 | simplifying with (2), (12), (23), (33), (34), (57), (61), (64) % 61.92/8.91 | gives: % 61.92/8.91 | (65) aElementOf0(all_33_1, all_35_0) % 61.92/8.91 | % 61.92/8.91 | GROUND_INST: instantiating (mMulComm) with xc, all_37_0, all_37_1, simplifying % 61.92/8.91 | with (2), (12), (25), (42), (44) gives: % 61.92/8.91 | (66) sdtasdt0(all_37_0, xc) = all_37_1 & $i(all_37_1) % 61.92/8.91 | % 61.92/8.91 | ALPHA: (66) implies: % 61.92/8.91 | (67) $i(all_37_1) % 61.92/8.91 | % 61.92/8.92 | GROUND_INST: instantiating (1) with xc, all_35_0, all_37_1, all_37_0, % 61.92/8.92 | simplifying with (2), (12), (23), (25), (33), (42), (44), (67) % 61.92/8.92 | gives: % 61.92/8.92 | (68) aElementOf0(all_37_1, all_35_0) % 61.92/8.92 | % 61.92/8.92 | BETA: splitting (31) gives: % 61.92/8.92 | % 61.92/8.92 | Case 1: % 61.92/8.92 | | % 61.92/8.92 | | (69) sdtasdt0(xz, xx) = all_39_0 & $i(all_39_0) & ~ % 61.92/8.92 | | aElementOf0(all_39_0, all_39_1) % 61.92/8.92 | | % 61.92/8.92 | | ALPHA: (69) implies: % 61.92/8.92 | | (70) ~ aElementOf0(all_39_0, all_39_1) % 61.92/8.92 | | (71) sdtasdt0(xz, xx) = all_39_0 % 61.92/8.92 | | % 61.92/8.92 | | REDUCE: (32), (70) imply: % 61.92/8.92 | | (72) ~ aElementOf0(all_39_0, all_35_0) % 61.92/8.92 | | % 61.92/8.92 | | GROUND_INST: instantiating (17) with all_37_1, all_39_0, xx, xz, simplifying % 61.92/8.92 | | with (26), (71) gives: % 61.92/8.92 | | (73) all_39_0 = all_37_1 % 61.92/8.92 | | % 61.92/8.92 | | REDUCE: (72), (73) imply: % 61.92/8.92 | | (74) ~ aElementOf0(all_37_1, all_35_0) % 61.92/8.92 | | % 61.92/8.92 | | PRED_UNIFY: (68), (74) imply: % 61.92/8.92 | | (75) $false % 61.92/8.92 | | % 61.92/8.92 | | CLOSE: (75) is inconsistent. % 61.92/8.92 | | % 61.92/8.92 | Case 2: % 61.92/8.92 | | % 61.92/8.92 | | (76) sdtpldt0(xx, xy) = all_39_2 & $i(all_39_2) & ~ % 61.92/8.92 | | aElementOf0(all_39_2, all_39_1) % 61.92/8.92 | | % 61.92/8.92 | | ALPHA: (76) implies: % 61.92/8.92 | | (77) ~ aElementOf0(all_39_2, all_39_1) % 61.92/8.92 | | (78) sdtpldt0(xx, xy) = all_39_2 % 61.92/8.92 | | % 61.92/8.92 | | REDUCE: (32), (77) imply: % 61.92/8.92 | | (79) ~ aElementOf0(all_39_2, all_35_0) % 61.92/8.92 | | % 61.92/8.92 | | GROUND_INST: instantiating (16) with all_33_1, all_39_2, xy, xx, simplifying % 61.92/8.92 | | with (19), (78) gives: % 61.92/8.92 | | (80) all_39_2 = all_33_1 % 61.92/8.92 | | % 61.92/8.92 | | REDUCE: (79), (80) imply: % 61.92/8.92 | | (81) ~ aElementOf0(all_33_1, all_35_0) % 61.92/8.92 | | % 61.92/8.92 | | PRED_UNIFY: (65), (81) imply: % 61.92/8.92 | | (82) $false % 61.92/8.92 | | % 61.92/8.92 | | CLOSE: (82) is inconsistent. % 61.92/8.92 | | % 61.92/8.92 | End of split % 61.92/8.92 | % 61.92/8.92 End of proof % 61.92/8.92 % SZS output end Proof for theBenchmark % 61.92/8.92 % 61.92/8.92 8318ms %------------------------------------------------------------------------------